\newproblem{lay:2_2_36}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.2.36}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Let $A=\begin{pmatrix}-25 & -9 & -27 \\ 536 & 185 & 537 \\ 154 & 52 & 143\end{pmatrix}$. Find the second and third columns of $A^{-1}$ without computing the first column.
}{
  % Solution
	Let us reduce the augmented matrix $\left(\begin{array}{c|cc}A &\mathbf{e}_1 &\mathbf{e}_2\end{array}\right)$.
	\begin{center}
		$\left(\begin{array}{rrr|rr}-25 & -9 & -27 & 0 & 0\\ 536 & 185 & 537 & 1 & 0\\ 154 & 52 & 143 & 0 & 1\end{array}\right) \sim 
		 \left(\begin{array}{rrr|rr}1& 0 & 0& 0.1126 & -0.1559 \\ 0 & 1 & 0 & -0.5611 & 1.0077 \\ 0 & 0 & 1 & 0.0828 & -0.1915\end{array}\right)$
	\end{center}
	The last two columns of the latter matrix are the two columns required by the problem.
}
\useproblem{lay:2_2_36}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
